In the preceding paper of this series [Leontidis, E.; Aroti, A.; Belloni, L. J. Phys. Chem. B 2009, 113, 14471, we considered and modeled the increase of the surface pressure of dipalmitoyl phosphatidylcholine (DPPC) monolayers over electrolyte solutions of various monovalent sodium salts. The experimental results for salts with large, less hydrophilic anions can be successfully described by models treating ionic specificity either as specific partitioning in the interfacial lipid layer or as a result of ion-lipid dispersion interactions. However, the results for salts with more hydrophilic anions, such as chloride and fluoride, cannot be fitted by any of these models, while they clearly demonstrate the existence of a specific sodium-DPPC interaction. In the present paper, we first prove that the experimental results for sodium fluoride (NaF) can be fitted by a model that is based on simultaneous complexation of sodium ions with up to three lipid molecules, as suggested by recent molecular dynamics simulations. We then return to the experimental results of sodium salts with more hydrophobic anions, treated in the preceding paper, and prove that these can be fitted equally well with a complex model, which accounts for both sodium complexation with the lipid head groups and anion partitioning within the lipid monolayers. The partitioning parameters obtained from this more complete model correlate well with several measures of ion specificity, such as ionic volume, von Hippel chromatographic parameters, or viscosity B-coefficients. A model for these partitioning chemical potentials is created based on the competition of cavity and ion hydration terms. The model leads to an excellent correlation of the partitioning chemical potentials with a function of the ionic radius, suggesting that specific anion effects on this lipid model system are mostly a matter of ionic size. Two notable exceptions from this correlation are thiocyanate and acetate ions, the charge distribution of which is not spherically symmetric, so that they are expected to have orientational-dependent interactions with the water-lipid interface. The implications of the present results on ion specificity in general are discussed.